683 research outputs found
Quantum number dimensional scaling analysis for excited states of multielectron atoms
A new dimensional scaling method for the calculation of excited states of
multielectron atoms is introduced. By including the principle and orbital
quantum numbers in the dimension parameter, we obtain an energy expression for
excited states including high angular momentum states. The method is tested on
He, Li, and Be. We obtain good agreement with more orthodox quantum mechanical
treatments even in the zeroth order.Comment: Submitted to Physical Review A, 13 pages, 6 Table
Fragments of ML Decidable by Nested Data Class Memory Automata
The call-by-value language RML may be viewed as a canonical restriction of
Standard ML to ground-type references, augmented by a "bad variable" construct
in the sense of Reynolds. We consider the fragment of (finitary) RML terms of
order at most 1 with free variables of order at most 2, and identify two
subfragments of this for which we show observational equivalence to be
decidable. The first subfragment consists of those terms in which the
P-pointers in the game semantic representation are determined by the underlying
sequence of moves. The second subfragment consists of terms in which the
O-pointers of moves corresponding to free variables in the game semantic
representation are determined by the underlying moves. These results are shown
using a reduction to a form of automata over data words in which the data
values have a tree-structure, reflecting the tree-structure of the threads in
the game semantic plays. In addition we show that observational equivalence is
undecidable at every third- or higher-order type, every second-order type which
takes at least two first-order arguments, and every second-order type (of arity
greater than one) that has a first-order argument which is not the final
argument
New analytical and numerical models of solar coronal loop: I. Application to forced vertical kink oscillations
Aims. We construct a new analytical model of a solar coronal loop that is
embedded in a gravitationally stratified and magnetically confined atmosphere.
On the basis of this analytical model, we devise a numerical model of solar
coronal loops. We adopt it to perform the numerical simulations of its vertical
kink oscillations excited by an external driver. Methods. Our model of the
solar atmosphere is constructed by adopting a realistic temperature
distribution and specifying the curved magnetic field lines that constitute a
coronal loop. This loop is described by 2D, ideal magnetohydro- dynamic
equations that are numerically solved by the FLASH code. Results. The vertical
kink oscillations are excited by a periodic driver in the vertical component of
velocity, acting at the top of the photosphere. For this forced driver with its
amplitude 3 km/s, the excited oscillations exhibit about 1.2 km/s amplitude in
their velocity and the loop apex oscillates with its amplitude in displacement
of about 100 km. Conclusions. The newly devised analytical model of the coronal
loops is utilized for the numerical simulations of the vertical kink
oscillations, which match well with the recent observations of decay-less kink
oscillations excited in solar loops. The model will have further implications
on the study of waves and plasma dynamics in coronal loops, revealing physics
of energy and mass transport mechanisms in the localized solar atmosphere.Comment: 6 Pages; 5 Figures; A&
Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels
We present simulation results of the impulsively generated linear and
non-linear Alfv\'en waves in the weakly curved coronal magnetic flux-tubes
(coronal funnels) and discuss their implications for the coronal heating and
solar wind acceleration. We solve numerically the time-dependent
magnetohydrodynamic (MHD) equations to obtain the temporal signatures of the
small (linear) and large-amplitude (non-linear) Alfv\'en waves in the model
atmosphere of expanding open magnetic field configuration (e.g., coronal
funnels) by considering a realistic temperature distribution. We compute the
maximum transversal velocity of both linear and non-linear Alfv\'en waves at
different heights in the coronal funnel, and study their response in the solar
corona during the time of their propagation. We infer that the pulse-driven
non-linear Alfv\'en waves may carry sufficient wave energy fluxes to heat the
coronal funnels and also to power the solar wind that originates in these
funnels. Our study of linear Alfv\'en waves show that they can contribute only
to the plasma dynamics and heating of the funnel-like magnetic flux-tubes
associated with the polar coronal holes.Comment: 16 pages of the text and 3 figure
Does the Sun Shrink with Increasing Magnetic Activity?
We have analyzed the full set of SOHO/MDI f- and p-mode oscillation
frequencies from 1996 to date in a search for evidence of solar radius
evolution during the rising phase of the current activity cycle. Like Antia et
al. (2000), we find that a significant fraction of the f-mode frequency changes
scale with frequency; and that if these are interpreted in terms of a radius
change, it implies a shrinking sun. Our inferred rate of shrinkage is about 1.5
km/y, which is somewhat smaller than found by Antia et al. We argue that this
rate does not refer to the surface, but rather to a layer extending roughly
from 4 to 8 Mm beneath the visible surface. The rate of shrinking may be
accounted for by an increasing radial component of the rms random magnetic
field at a rate that depends on its radial distribution. If it were uniform,
the required field would be ~7 kG. However, if it were inwardly increasing,
then a 1 kG field at 8 Mm would suffice.
To assess contribution to the solar radius change arising above 4Mm, we
analyzed the p-mode data. The evolution of the p-mode frequencies may be
explained by a magnetic^M field growing with activity. The implications of the
near-surface magnetic field changes depend on the anisotropy of the random
magnetic field. If the field change is predominantly radial, then we infer an
additional shrinking at a rate between 1.1-1.3 km/y at the photosphere. If on
the other hand the increase is isotropic, we find a competing expansion at a
rate of 2.3 km/y. In any case, variations in the sun's radius in the activity
cycle are at the level of 10^{-5} or less, hence have a negligible contribution
to the irradiance variations.Comment: 10 pages (ApJ preprint style), 4 figures; accepted for publication in
Ap
Spectroscopic Observations and Modelling of Impulsive Alfv\'en Waves Along a Polar Coronal Jet
Using the Hinode/EIS 2 spectroscopic observations, we study the intensity,
velocity, and FWHM variations of the strongest Fe XII 195.12 \AA\ line along
the jet to find the signature of Alfv\'en waves. We simulate numerically the
impulsively generated Alfv\'en waves within the vertical Harris current-sheet,
forming the jet plasma flows, and mimicking their observational signatures.
Using the FLASH code and the atmospheric model with embedded weakly expanding
magnetic field configuration within a vertical Harris current-sheet, we solve
the two and half-dimensional (2.5-D) ideal magnetohydrodynamic (MHD) equations
to study the evolution of Alfv\'en waves and vertical flows forming the plasma
jet. At a height of from the base of the jet, the
red-shifted velocity component of Fe XII 195.12 \AA\ line attains its maximum
() which converts into a blue-shifted one between the
altitude of . The spectral intensity continously increases up
to , while FWHM still exhibits the low values with almost
constant trend. This indicates that the reconnection point within the jet's
magnetic field topology lies in the corona from its
footpoint anchored in the Sun's surface. Beyond this height, FWHM shows a
growing trend. This may be the signature of Alfv\'en waves that impulsively
evolve due to reconnection and propagate along the jet. From our numerical
data, we evaluate space- and time- averaged Alfv\'en waves velocity amplitudes
at different heights in the jet's current-sheet, which contribute to the
non-thermal motions and spectral line broadening. The synthetic width of Fe XII
line exhibits similar trend of increment as in the
observational data, possibly proving the existence of impulsively generated (by
reconnection) Alfv\'en waves which propagate along the jet
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